On Basener and Sanford’s paper falsifying Fisher’s Darwinism theorem: It will be no small thing to make reality matter again

Due to the tradition of professional scientific writing, major developments in scientific literature often arrive muffled in language so bland or technical as to be totally missed by a general reader. This, along with the media’s habit of covering up for evolution, is how large cracks in the foundation of Darwinism spread unnoticed by the public, which goes on assuming that the science is all settled and will ever remain so.

A case in point is a recent article in the Journal of Mathematical Biology, a significant peer-reviewed publication from the influential publisher Springer. The title of the article announces, “The fundamental theorem of natural selection with mutations.”

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Fisher’s theorem, offered as what amounts to a “mathematical proof that Darwinian evolution is inevitable,” now stands as falsified.

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Kudos to Basener and Sanford for making this important point. Now, will the textbooks and the online encyclopedia articles take note? More.

In short, no.

What is not falsified — and cannot be falsified either by mathematics or by reality-based thinking — is the Darwinjobs in education, the Darwinblather in science media, and the Darwinfunding for questionable projects because, well – to doubt Darwin is to be “against science,” right?

Of course, at some point, we will have honest discussions again. Godspeed to those trying to make it happen just now.

See also: Fisher’s proof of Darwinism flipped: Basener replies to Erasmus Wiffball: Fisher attempted to prove that Mendelian genetics logically must lead to a Darwinist evolution. He believed that he was successful and along the way he (co)invented population genetics and modern statistics. However, took 40-80 years for people to realize he did not achieve his original goal. His attempt to “prove Darwin from Mendel” however did give a framework for connecting Mendelian discrete genetics with gradual change in observed traits across a population.

Fisher’s Proof of Darwinism Flipped: William Basener replies to Bob O’Hara. The mutation rate used in the paper is 1 mutation per generation. As with all the parameters in the paper we chose this parameter so that if there is any bias, the parameter selection favors selection and increasing fitness.

2 Replies to “On Basener and Sanford’s paper falsifying Fisher’s Darwinism theorem: It will be no small thing to make reality matter again”

The principal roles of mathematical proof in science are to establish the internal consistency of explanations and to derive the logical consequences of explanations. The logical consequences are sometimes empirically testable.

Basically, the proofs address what the scientists are saying. “Are we contradicting ourselves? If our explanation is correct, then what else should we expect to observe?” Scientists do not use mathematics to establish what is “really real.”

If you see mathematics treated as the arbiter of reality, then you can be sure that you’re dealing with metaphysics, not science. There are elements of metaphysics in ID (see William Dembski’s Being as Communion: A Metaphysics of Information), and it is understandable that many followers of ID, lacking in scientific training, should be unclear as to where science ends and metaphysics begins.

Ronald Fisher’s “Fundamental” Theorem of Natural Selection, as formalized by others, is mathematically correct, but also practically unimportant. The main problem is that it hinges on simplifying assumptions that, contrary to Fisher’s belief in 1930, generally do not comport with biological reality.

As George Box observed, “In essence, all models are wrong, but some are useful.” The tacit model in Fisher’s FTNS is, from what I have read, too wrong in most real-world circumstances to be useful. Again, the wrongness is not mathematical incorrectness, but instead mismatch of underlying assumptions to evolutionary systems in nature. It is vital to note, though the point is somewhat subtle, that the model is useful to theoretical biologists, who seek to understand evolutionary systems in abstraction. That is, there are many models in theoretical biology that are too simple to account well for biological reality, but that are part of a general comprehension of how biological systems “work.”

In “The Fundamental Theorem of Natural Selection with Mutations,” Basener and Sanford develop a model that they regard as an extension of the model tacit in Fisher’s FTNS. One should not assume that the reviewers and editors of The Journal of Mathematical Biology judged the work of Basener and Sanford to be of more than theoretical interest. The scientific question, as with the original model, is whether the assumptions comport with evolutionary systems in nature. And that question comes, of course, with the question of how to determine, by empirical observation, the degree to which the assumptions hold.

The simulations of Basener and Sanford are, if their software correctly implements their model, proofs of the logical consequences of their model (for particular cases). Do evolutionary systems in nature behave similarly to the simulated systems? Well, that’s an odd question, because Basener and Sanford have simulated haploid organisms. And the oddness underscores the point that theoretical biologists are commonly interested in evolutionary systems that are not in close correspondence with those that exist in nature.

The significance of the work of Basener and Sanford is, at present, strictly theoretical, not practical. The appropriate quantitative measure of the significance is not the number of times the paper is downloaded, but instead the number of times the paper is cited in the peer-reviewed literature. (For instance, the greatest number of citations for any of the papers of Dembski and Marks is, according to Google Scholar, 36. Subtracting self-citation and citation outside the peer-reviewed literature, there are about 20 citations left. In contrast, one of Joe Felsenstein’s papers presently has 34,734 citations.) I invite Ms. O’Leary to mark the publication date of the paper as Basener-Sanford Day (never to be abbreviated), and to report each year how many citations the paper has garnered.

As for the significance of Fisher’s FTNS, it was never foundational. It may have played a significant rhetorical role in the arguments that a synthesis of Darwinian theory and population genetics had been achieved. (I’m no more an expert on the matter than William Basener is.) But the fact of the matter is that there was, for decades, no general understanding of what Fisher had meant to say. Neither Darwinian theory nor population genetics was founded on the FTNS.

Erasmus Wiffball, thank you for stopping by and for your thoughtful and detailed comments. Just a few thoughts:

1. I quite like these points you made:

“If you see mathematics treated as the arbiter of reality, then you can be sure that you’re dealing with metaphysics, not science.”

“The main problem is that [Fisher’s theorem] hinges on simplifying assumptions that, contrary to Fisher’s belief in 1930, generally do not comport with biological reality.”

“The scientific question, as with the original model, is whether the assumptions comport with evolutionary systems in nature. And that question comes, of course, with the question of how to determine, by empirical observation, the degree to which the assumptions hold.”

These are excellent cautions. They remind me of computer simulations generally, including recent and much-touted evolutionary algorithms.

2. As for Box’s observation, “In essence, all models are wrong, but some are useful,” this is no doubt true in the sense that no model fully and comprehensively simulates reality.

My unease with Box’s statement, however, is that over the years this statement has regularly been used as a fig leaf to cover glaring problems with models. The statement seems to serve as a ready-made excuse for a poorly-developed model, pulled out when needed to defend a model against criticism.

Does my model produce correct conclusions? No. Does it accurately reflect reality? No. But, hey, it is still “useful.” Not so much because it teaches us anything significant about reality. Not because it helps us get to the truth. Rather, because: (i) it allows me to start thinking about the issues, even if inaccurately and incompletely (this is good), (ii) it allows me to make a claim I wanted to make but couldn’t make with real observations (this is suspect), and, permit me to be a bit more cynical, (iii) it keeps my name in the public eye, the funds flowing, and the lights on (this is not good). Furthermore, if my math is “correct” (meaning, simply, no errors in the calculations put forward), then I get to put the stamp of mathematical approval on my claims.

I don’t know if this is too cynical or if this expresses part of what you were driving at. Yes, the math needs to be “correct”. But where the rubber meets the road is, as you say, in the assumptions underlying the model. It sounds like Fisher’s model suffers significantly in this regard. I haven’t looked at Basener and Sanford’s work yet, but they should be held to a similar standard.

One caveat:

We need to carefully identify the claim flowing from each model. If Scientist A claims that his model reflects a broad-ranging principle that applies across biology, and Scientist B later claims that his model demonstrates that Scientist A’s model doesn’t work in a particular case, then it isn’t a valid criticism of Scientist B’s work to note that Scientisit B’s model also does not work across biology as a whole.

Again, I haven’t delved into the two enough to know what we are dealing with in the present situation, but we need to be careful to not assume that equivalent claims (and therefore equivalent demand for support and scope) are in play.

3. Also, it wasn’t clear what you meant by “. . . it is understandable that many followers of ID, lacking in scientific training, should be unclear as to where science ends and metaphysics begins.”

Are you referring to any particular instance you could share? Are you suggesting that this failure to distinguish between where the science ends and the metaphysics ends is largely absent among those with “scientific training,” particularly in the field of evolutionary theory? Just curious what your intent was with that statement.

4. Finally, I have no particular horse in the race about whether Basener and Sanford will become widely cited, but I certainly hope you don’t mean to imply that the number of citations is a good litmus test for whether something is true? Yes, it might give us a sense as to how often a particular theory or claim has come up in conversation or in the broader consciousness of the community doing the citing, but that is quite different from whether we should take the cited content seriously.